Sadly, it's funnier than that. What you just said but it happened at least three times. A now defunct club named Tiburones Rojos de Veracruz was involved in at least two of those.
Back in the day the way to cuck teams that earned their promotion was to say that they didn't have big enough stadiums. The method you are describing is team that earns its promotion gets bought by owner of failing team and both teams swap everything. There's also, my team doesn't get promoted naturally so I just buy one that is already in the top flight. For American context is like what was done to the Cleveland Spiders ages ago, one team becomes the farm system of the other. Mexican teams are called franchises more often than they are called clubs because much like American sports teams half of them have moved at least once.
Funniest part? Liga MX has been devoid of promotion and relegation for years now even though they have functional lower leagues. They just became the MLS but shitier. Mexico can play football, they just cuck their talented youths until they are forced into getting normie jobs.